Integrates 3
Periodic functions day 2
Name
Date
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Objective: To find the amplitude and period of trigonometric function from its equation; to find the amplitude and period of a
trigonometric function from its graph to graph sine and cosine functions with various amplitudes and periods.
Real world applications: “Amplitude and frequency are important concepts that are essential to the understanding of many
fields, including music.”
“The loudness or amplitude, or a musical sound is a comparative measure of the strength of the sound that is heard. Loudness
is related to the distance from the source and the energy of the vibration.”
“Pitch is determined by the number of vibrations per second, or the frequency of the vibrations that yield a sound wave.
Frequency is the reciprocal of the period.”
Resource: Hayden, Jerome D. and Hall Betty C. (1993). Trigonometry, Prentice Hall; Englewood Cliffs, New Jersey.
Practice graphing periodic functions with different values for „amplitude‟ (A)
Given: the graph is f(x) = sin(x)
Graph f(x) = 2sin(x) on
the same graph
Graph f(x) = 0.5sin(x) on
the same graph
Graph f(x) = -sin(x) on
the same graph
Results compared to f(x) = sin(x):
What happened when A = 2
What happened when A = 0.5
What happened when A = -1
Using the vocabulary from this unit A does what to the curve?
Practice graphing periodic functions with different values for „period‟ (B)
Given: the graph is f(x) = sin(x)
Graph f(x) = sin(2x) on
the same graph
Graph f(x) = sin(0.5x) on
the same graph
Graph f(x) = sin(-x) on
the same graph
Results compared to f(x) = sin(x):
What happened when B = 2
What happened when B = 0.5
What happened when B = -1
Using the vocabulary from this unit B does what to the curve?
Now lets practice calculating period given a function:
period 
2

B